Sample Variance Under Serial Correlation
Three observations X₁, X₂, X₃ each have mean μ and variance 1, with Corr(Xᵢ, Xⱼ) = (1/2)^|i − j| (a first-order autoregressive pattern). Let S² = (1/2) Σ (Xᵢ − X̄)². Find E[S²] as a reduced fraction.
Related problems & prerequisites
Worth solving first
- Variance of Two Dice 2.0/10
Source: Original problem written for AxiomIQ; expectation of the sample variance for dependent data.